Subtract the monthly fee:
10.58 -5 = 5.58
Divide the remaining amount by cost per minute:
5.58/ 0.09 = 62
He was billed for 62 minutes.
Which statements are true regarding the system of equations? Check all that apply. 8 x + 10 y = 30. 12 x + 15 y = 60. The lines coincide. The lines are parallel. The slopes are equal. The y-intercepts are different. The system has one solution. The system has an infinite number of solutions. The system has no solution. Mark this and return
Answer: The lines are parallel.
The slopes are equal.
The y-intercepts are different.
The system has no solution.
Step-by-step explanation:
For a pair of equations: [tex]a_1x+b_1y=c_1\\\\a_2x+b_2y=c_2[/tex]
They coincide if [tex]\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}=\dfrac{c_1}{c_2}[/tex]
They are parallel if [tex]\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}\neq\dfrac{c_1}{c_2}[/tex]
They intersect if [tex]\dfrac{a_1}{a_2}\neq\dfrac{b_1}{b_2}[/tex]
Given equations: [tex]8 x + 10 y = 30\\ 12 x + 15 y = 60[/tex]
Here,
[tex]\dfrac{a_1}{a_2}=\dfrac{8}{12}=\dfrac{2}{3}\\\\ \dfrac{b_1}{b_2}=\dfrac{10}{15}=\dfrac{2}{3}\\\\ \dfrac{c_1}{c_2}=\dfrac{30}{60}=\dfrac{1}{2}[/tex]
⇒[tex]\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}\neq\dfrac{c_1}{c_2}[/tex]
Hence, The lines are parallel.
It has no solution. [parallel lines have no solution]
Write 8 x + 10 y = 30 in the form of y= mx+c, where m is slope and c is the y-intercept.
[tex]y=-\dfrac{8}{10}x+\dfrac{30}{10}\Rightarrow\ y=-0.8x+3[/tex]
i.e. slope of 8 x + 10 y = 30 is -0.8 and y-intercept =3
Write 12 x + 15 y = 60 in the form of y= mx+c, where m is slope
[tex]y=-\dfrac{12}{15}x+\dfrac{60}{15}\Rightarrow\ y=-0.8x+4[/tex]
i.e. slope of 12 x + 15 y = 60 is -0.8 and y-intercept =4
i.e. The slopes are equal but y-intercepts are different.
Answer: The lines are parallel.
The slopes are equal.
The y-intercepts are different.
The system has no solution.
Step-by-step explanation:
For a pair of equations:
They coincide if
They are parallel if
They intersect if
Given equations:
Here,
⇒
Hence, The lines are parallel.
It has no solution. [parallel lines have no solution]
Write 8 x + 10 y = 30 in the form of y= mx+c, where m is slope and c is the y-intercept.
i.e. slope of 8 x + 10 y = 30 is -0.8 and y-intercept =3
Write 12 x + 15 y = 60 in the form of y= mx+c, where m is slope
i.e. slope of 12 x + 15 y = 60 is -0.8 and y-intercept =4
i.e. The slopes are equal but y-intercepts are different.
The mode of the numbers 1,1,3,3, 5, 6, 6, 6, 7, 8 is
Answer:
The mode of the above is 6.
Step-by-step explanation:
Mode-the number that occurs most frequently in a set of numbers.
The six appeared three times being the most.
I really hope this helps.
can anyone help me with this ?
Answer: x=35
Step-by-step explanation:
There are 720 degrees total in a hexagon. So, all of the angles should add up to that. Write out the equation
720= (4x-5)+(117)+(3x-3)+(3x+6)+(118)+(4x-3)
720=14x+230
490=14x
x=35
hope this helped you:)
Which sum or difference is modeled by the algebra tiles?
Answer:
(C)[tex]x^2+4x-2-(-x^2+2x-4)=2x^2+2x+2[/tex]
Step-by-step explanation:
The expression represented by the upper tiles is: [tex]x^2+4x-2[/tex]
The expression represented by the lower tiles is: [tex]x^2-2x+4[/tex]
Adding the two
[tex]x^2+4x-2+(x^2-2x+4)=2x^2+2x+2[/tex]
Writing it as a difference, we have:
[tex]x^2+4x-2-(-x^2+2x-4)=2x^2+2x+2[/tex]
The correct option is C.
Answer:
yeah, what newton said :]
Find the probability of selecting none of the correct six integers in a lottery, where the order in which these integers are selected does not matter, from the positive integers not exceeding the given integers. (Enter the value of probability in decimals. Round the answer to two decimal places.) 40
Answer:
Probability of selecting none of the correct six integers:
a) 0.350
b) 0.427
c) 0.489
d) 0.540
Step-by-step explanation:
a) 40
Given:
Number of integers in a lottery 6
Order in which these integers are selected does not matter
To find:
Probability of selecting none of the correct six integers
Solution:
When the order of selection does not matter then we use Combinations.
Given integers = 40
Number of ways to choose 6 from 40.
Let A be the sample space of choosing digits 6 from 40.
Then using Combinations:
(n,k) = n! / r! (n-r)!
n = 40
r = 6
40C6
=(40,6) = 40! / 6! ( 40 - 6)!
= 40! / 6!34!
= 40*39*38*37*36*35*34! / 6!34!
= 2763633600 / 720
= 3838380
Let E be the event of selecting none of the correct six integers.
So using combinations we can find the total number of ways of selecting none of 6 integers from 40
n = 40 - 6 = 34
r = 6
34C6
=(34,6) = 34! / 6! ( 34 - 6)!
= 34! / 6! 28!
= 34 * 33 * 32 * 31 * 30 * 29 * 28! / 6! 28!
=968330880 / 720
= 1344904
Probability of selecting none of the correct six integers:
P(E) = E / A
= 1344904 / 3838380
= 0.350
Probability of selecting none of the correct six integers is 0.350
b) 48
Following the method used in part a)
(n,k) = n! / r! (n-r)!
n = 48
r = 6
48C6
=(48,6) = 48! / 6! ( 48 - 6)!
= 48! / 6! ( 42 )!
= 48*47*46*45*44*43*42! / 6!42!
= 8835488640 / 720
= 12271512
Let E be the event of selecting none of the correct six integers.
So using combinations we can find the total number of ways of selecting none of 6 integers from 48
n = 48 - 6 = 42
r = 6
42C6
= (42,6) = 42! / 6! ( 42 - 6)!
= 42! / 6! 36!
= 3776965920
= 5245786
P(E) = E / A
= 5245786/12271512
= 0.427
c) 56
(n,k) = n! / r! (n-r)!
n = 56
r = 6
56C6
=(56,6) = 56! / 6! ( 56- 6)!
= 56! / 6! ( 50 )!
= 56*55*54*53*52*51*50! / 6! 50!
= 23377273920/6
= 32468436
Let E be the event of selecting none of the correct six integers.
So using combinations we can find the total number of ways of selecting none of 6 integers from 56
n = 56 - 6 = 50
(50,6) = 50! / 6! ( 50- 6)!
= 50*49*48*47*46*45*44! / 44! 6!
= 11441304000 / 6
= 15890700
P(E) = E / A
= 15890700 / 32468436
= 0.489
d) 64
(n,k) = n! / r! (n-r)!
n = 64
r = 6
64C6
=(64,6) = 64! / 6! ( 64 - 6)!
= 64! / 6! ( 58 )!
= 64*63*62*61*60*59*58! / 6! 58!
= 53981544960 / 720
= 74974368
Let E be the event of selecting none of the correct six integers.
So using combinations we can find the total number of ways of selecting none of 6 integers from 64
n = 64 - 6 = 58
(58,6) = 58! / 6! ( 58- 6)!
= 58*57*56*55*54*53*52! / 52! 6!
= 29142257760/ 6
= 40475358
P(E) = E / A
= 40475358/ 74974368
= 0.540
The probability of selecting none of the correct six integers in a lottery is, 0.350.
Number of integers given = 40
So, Total outcomes for choosing 6 from 40 integers.
Number of arrangements [tex]=_{6}^{40}\textrm{C}[/tex]
[tex]=\frac{40!}{6!*34!} =3838380[/tex]
Since, we have to find probability of selecting none of the correct six integers in a lottery.
Remaining integer = 40 - 6 =34
Let favourable outcomes is selecting none of the correct six integers.
So, number of arrangements, = [tex]=_{6}^{34}\textrm{C}[/tex]
= [tex]\frac{34!}{6!*28!}=1344904[/tex]
Probability is defined as, divide favourable outcomes by total outcomes.
So, The probability of selecting none of the correct six integers in a lottery,
[tex]P=\frac{1344904}{3838380}=0.35[/tex]
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On a coordinate plane, kite K L M N is shown. Point K is at (5, 3), point L is at (3, 2), point M is at (2, 3), and point N is at (3, 4). What is the perimeter of kite KLMN? StartRoot 2 EndRoot + StartRoot 5 EndRoot units StartRoot 14 EndRoot units 2 StartRoot 2 EndRoot + 2 StartRoot 5 EndRoot units 4 StartRoot 5 EndRoot units HELP PLEASE
Answer:
[tex]2\sqrt{2} +2\sqrt{5}[/tex]
Step-by-step explanation:
i just got this one right
the kite has two pairs of congruent sides. using the distance formula, the two shorter sides=[tex]\sqrt{2}[/tex] (since there are two of those length sides, you multiply it by two). Again with the distance formula, the two longer sides=[tex]\sqrt{5}[/tex] (also multiply this by two).this gives the answer c or [tex]2\sqrt{2}+2\sqrt{5}[/tex]
Answer:
The answer is c [tex]\sqrt[2]{2}[/tex] + [tex]\sqrt[2]{5}[/tex] units. just took the test
Step-by-step explanation:
Two angles form a linear pair. The measure of one angle is x and the measure of the other angle is 1.4 times x plus 12∘ . Find the measure of each angle.
Answer:
70° and 110°
Step-by-step explanation:
If two angles forms a linear pair, this means that the sum of the angles is 180°. If the measure of one angle is x and the measure of the other angle is 1.4 times x plus 12∘
Let A be the first angle = x°
Let B be the second angle = (1.4x+12)°
Since they form a linear pair, then
A+B = 180°
x + 1.4x+12 = 180°
2.4x = 180-12
2.4x = 168
x = 168/2.4
x = 70°
The measure of angle A = 70°
The measure if angle B = 1.4x+12
B = 1.4(70)+12
B = 98+12
B = 110°
The measure of both angles are 70° and 110°
Write an inequality:
from (–5) to (–1) inclusive
Answer:
Inclusive means that we'll use the signs ≤ and ≥. Let's call the variable in our inequality as x. Therefore, the answer is -5 ≤ x ≤ -1.
I WILL MARK THE BRAINLIEST! please help me
There are 200 students in 8th grade. There are 3 different elective classes. All 8th grade students must take at least one elective.
- 35 total students are in drama
- 75 total students are in cooking
- 15 students are in both drama and P.E
-10 Students are in drama and cooking
- 5 students are in P.E and cooking
- 8 students are in all three electives
How many students are in P.E?
How many are ONLY in P.E?
Please answer both questions in two sentences.
Answer:
How many students are in P.E? 90
How many are ONLY in P.E? 62
Step-by-step explanation:
How many students are in P.E?
200 students in 8th grade.
35=drama
75=cooking
200-110=90=PE.
How many are ONLY in P.E?
Within 90 students, 15 is also in drama, with 5 is also in cooking, and 8 is in all of 3. =28.
90-28=62
Hope this helps!
On a coordinate plane, a piecewise function has 3 lines. The graph shows cleaning time in hours on the x-axis and total cost in dollars on the y-axis. The first line has an open circle at (0, 50) and continues horizontally to a closed circle at (2, 50). The second line has an open circle at (2, 100) and continues horizontally to a closed circle at (6, 100). The third line has an open circle at (6, 200) and continues horizontally to a closed circle at (8, 200). The graph represents the cleaning costs charged by a housekeeping service. Which statement is true of the cost function? A cleaning time of 2 hours will cost $100. A cleaning time of 6 hours will cost $150. Cost is a fixed rate of $100 for jobs requiring more than 2 hours, up to a maximum of 6 hours. Cost is a fixed rate of $200 for jobs that require at least 6 hours.
Answer:
C. (2, 6] hour jobs cost $100
Step-by-step explanation:
Let's consider each of these statements in view of the graph:
A cleaning time of 2 hours will cost $100. -- The closed circle at (2, 50) tells you the cost of a 2-hour job is $50, not $100.A cleaning time of 6 hours will cost $150. -- The closed circle at (6, 100) tells you the cost of a 6-hour job is $100, not $150.Cost is a fixed rate of $100 for jobs requiring more than 2 hours, up to a maximum of 6 hours. -- The line between the open circle at (2, 100) and the closed circle at (6, 100) tells you this is TRUE.Cost is a fixed rate of $200 for jobs that require at least 6 hours. -- "At least 6 hours" means "greater than or equal to 6 hours." The closed circle at (6, 100) means a 6-hour job is $100, not $200.Answer:
(0,8) first option and 50,100 or 200 in the second option
Step-by-step explanation:
Write as an equation: Alice, Barbara, and Carol are sisters. Alice is 3 years younger than Barbara, and Barbara is 5 years younger than Carol. Together the sisters are 68 years old. How old is Barbara? (Let b = Barbara)
a+b+c=68
b-3=a
c-5=b
now just solve the system of equations, substitue so that there are only b's in the equation:
a+b+c=68
(b-3) + b + (b+5) = 68
3b=66
b=22
Therefore Barbara is 22
The required age of barbar is 22 years.
Alice, Barbara, and Carol are sisters. Alice is 3 years younger than Barbara, and Barbara is 5 years younger than Carol. Together the sisters are 68 years old. How old is Barbara to be determined.
What is arithmetic?In mathematics, it deals with numbers of operations according to the statements.
Let the age of Alice, Barbara and Carol are a, b and c.
Age Alice is 3 years younger than Barbara,
a = b - 3 - - - -(1)
Age Barbara is 5 years younger than Carol
b = c - 5
c = b + 5 - - - -(2)
Together the sisters are 68 years old i.e.
a + b +c =68
From equation 1 and 2
b - 3 + b + b +5 = 68
3b + 2 = 68
3b = 66
b = 33
Thus, the required age of barbar is 22 years.
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A plane started on a flight at 9:30 a.m and arrived at its destination at 1:45pm. The plane used 51 gallons of gas. The number of gallons used per hour was
Will mark Brainlist
Answer:
12 gallons per hour
Step-by-step explanation:
Given the following :
Start time of flight = 9:30 a.m
Arrival time of flight = 1:45p.m
Gallons of gas used during duration of flight = 51 gallons
Number of hours spent during flight:
Arrival time - start time
1:45 pm - 9:30 am = 4hours and 15minutes
4hours 15minutes = 4.25hours
If 4.25hours requires 51 gallons of gas;
Then 1 hour will require ( 51 / 4.25)gallons
= 51 / 4.25
= 12 gallons
The tee for the fifth hole on a golf course is 375 yards from the tee. On that hole, Marsha hooked her ball to the left, as sketched below. Find the distance between Marsha’s ball and the hole to the nearest tenth of a yard.
Answer:
158.73 yd
Step-by-step explanation:
A picture of the situation is needed, investigating I could find a related one, in the same way the important thing is the solution, the data can be exchanged. I attach the drawing.
Let use the formula of the law of cosine:
c ^ 2 = a ^ 2 + b ^ 2 - 2 * a * b * cos C, to solve the problem
Let the third side be c, we replace:
c ^ 2 = 375 ^ 2 + 240 ^ 2 - 2 * 375 * 240 * cos 16 °
c ^ 2 = 198225 - 173027.10
c ^ 2 = 25197.9
c = 158.73
So the distance is 158.73 yd
Answer: the right answer is 195.4
Step-by-step explanation: this guy does not what's happening
Enter the correct answer in the box. What is the standard form of function
Answer:
f(x) = 4x² + 48x + 149
Step-by-step explanation:
Given
f(x) = 4(x + 6)² + 5 ← expand (x + 6)² using FOIL
= 4(x² + 12x + 36) + 5 ← distribute parenthesis by 4
= 4x² + 48x + 144 + 5 ← collect like terms
= 4x² + 48x + 149 ← in standard form
Answer:
[tex]f(x)=4x^{2} +149[/tex]
Step-by-step explanation:
Start off by writing the equation out as it is given:
[tex]f(x)=4(x+6)^{2} +5[/tex]
Then, get handle to exponent and distribution of the 4 outside the parenthesis:
[tex]f(x)=4(x^{2} +36)+5\\f(x)=4x^{2} +144+5[/tex]
Finally, combine any like terms:
[tex]f(x)=4x^{2} +149[/tex]
Find the product.
(5ab3b) (2ab)
PLEASE HELP!!! ASAP!!!
Answer:
10a²b²6ab²
Step-by-step explanation:
Distribute the 2ab the other values
Instructions: Find the missing side. Round your answer to the
nearest tenth
Answer:
x = 50°Step-by-step explanation:
To find x we use cosine
cos ∅ = adjacent / hypotenuse
From the question
The hypotenuse is x
The adjacent is 18
So we have
cos 69 = 18/x
x cos 69 = 18
Divide both sides by cos 69
x = 18/cos 69
x = 50.2
x = 50° to the nearest tenth
Hope this helps you
The confidence interval for the water consumption of a certain plant is 5 gallons to 13 gallons per year. The level of confidence is 95%. What is the average consumption and the margin of error?
Answer:
Average consumption ( mean ) = 9
MOE = 4
Step-by-step explanation:
We know that
CI ( 5 ; 13 )
and CI [ μ - MOE ; μ + MOE ]
From the above relations we get
μ - MOE = 5
μ + MOE = 13
Adding member to member these two equations we get
2*μ = 18
μ = 9 and MOE = 13 - 9
MOE = 4
BRAINLEST Use the function f(x) = 2x^2 − 5x + 3 to answer the questions. Part A: Completely factor f(x). Part B: What are the x-intercepts of the graph of f(x)? Show your work.
Answer:
answer pic below :)
Step-by-step explanation:
In65 - lnX = 39
What does X=?
Answer:
The answer is 7.47Step-by-step explanation:
In this problem we are going find the natural logarithmic of the numbers involved and solve for x
[tex]ln65-Ln x= 39\\[/tex]
from tables
ln 65= 4.17[tex]4.17-ln x= 39\4.17-39= lnx\\-34.83=lnx\\[/tex]
taking the exponents of both sides we have
[tex]e^-^3^4^.^8^3= x\\x= 7.47[/tex]
[tex]Let $u$ and $v$ be the solutions to $3x^2 + 5x + 7 = 0.$ Find\[\frac{u}{v} + \frac{v}{u}.\][/tex]
By the factor theorem,
[tex]3x^2+5x+7=3(x-u)(x-v)\implies\begin{cases}uv=\frac73\\u+v=-\frac53\end{cases}[/tex]
Now,
[tex](u+v)^2=u^2+2uv+v^2=\left(-\dfrac53\right)^2=\dfrac{25}9[/tex]
[tex]\implies u^2+v^2=\dfrac{25}9-\dfrac{14}3=-\dfrac{17}9[/tex]
So we have
[tex]\dfrac uv+\dfrac vu=\dfrac{u^2+v^2}{uv}=\dfrac{-\frac{17}9}{\frac73}=\boxed{-\dfrac{17}{21}}[/tex]
The value of [tex]\frac{u}{v} +\frac{v}{u}[/tex] is [tex]\frac{-17}{21}[/tex].
What is quadratic equation?A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is[tex]ax^{2} +bx+c=0[/tex], where a and b are the coefficients, x is the variable, and c is the constant term.
What is the sum and product of the roots of the quadratic equation?If [tex]ax^{2} +bx+c = 0[/tex] be the quadratic equation then
Sum of the roots = [tex]\frac{-b}{a}[/tex]
And,
Product of the roots = [tex]\frac{c}{a}[/tex]
According to the given question.
We have a quadratic equation [tex]3x^{2} +5x+7=0..(i)[/tex]
On comparing the above quadratic equation with standard equation or general equation [tex]ax^{2} +bx+c = 0[/tex].
We get
[tex]a = 3\\b = 5\\and\\c = 7[/tex]
Also, u and v are the solutions of the quadratic equation.
⇒ u and v are the roots of the given quadratic equation.
Since, we know that the sum of the roots of the quadratic equation is [tex]-\frac{b}{a}[/tex].
And product of the roots of the quadratic equation is [tex]\frac{c}{a}[/tex].
Therefore,
[tex]u +v = \frac{-5}{3}[/tex] ...(ii) (sum of the roots)
[tex]uv=\frac{7}{3}[/tex] ....(iii) (product of the roots)
Now,
[tex]\frac{u}{v} +\frac{v}{u} = \frac{u^{2} +v^{2} }{uv} = \frac{(u+v)^{2}-2uv }{uv}[/tex] ([tex](a+b)^{2} =a^{2} +b^{2} +2ab[/tex])
Therefore,
[tex]\frac{u}{v} +\frac{v}{u} =\frac{(\frac{-5}{3} )^{2}-2(\frac{7}{3} ) }{\frac{7}{3} }[/tex] (from (i) and (ii))
⇒ [tex]\frac{u}{v} +\frac{v}{u} =\frac{\frac{25}{9}-\frac{14}{3} }{\frac{7}{3} }[/tex]
⇒ [tex]\frac{u}{v} +\frac{v}{u} = \frac{\frac{25-42}{9} }{\frac{7}{3} }[/tex]
⇒ [tex]\frac{u}{v} +\frac{v}{u} = \frac{\frac{-17}{9} }{\frac{7}{3} }[/tex]
⇒ [tex]\frac{u}{v} +\frac{v}{u} =\frac{-17}{21}[/tex]
Therefore, the value of [tex]\frac{u}{v} +\frac{v}{u}[/tex] is [tex]\frac{-17}{21}[/tex].
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Can someone help me on this finance problem?
Jane wants to estimate the proportion of students on her campus who eat cauliflower. After surveying 24 students, she finds 2 who eat cauliflower. Obtain and interpret a 95% confidence interval for the proportion of students who eat cauliflower on Jane's campus using Agresti and Coull's method.
Construct and interpret the 95% confidence interval. Select the correct choice below and fill in the answer boxes within your choice.
(Round to three decimal places as needed.)
A. The proportion of students who eat cauliflower on Jane's campus is between___ and __ 95% of the time.
B.There is a 95% chance that the proportion of students who eat cauliflower in Jane's sample is between __ and __.
C. There is a 95% chance that the proportion of students who eat cauliflower on Jane's campus is between __ and__.
D. One is 95% confident that the proportion of students who eat cauliflower on Jane's campus is between __ and __.
Answer:
A 95% confidence interval for the proportion of students who eat cauliflower on Jane's campus is [0.012, 0.270].
Step-by-step explanation:
We are given that Jane wants to estimate the proportion of students on her campus who eat cauliflower. After surveying 24 students, she finds 2 who eat cauliflower.
Firstly, the pivotal quantity for finding the confidence interval for the population proportion is given by;
P.Q. = [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = sample proportion of students who eat cauliflower
n = sample of students
p = population proportion of students who eat cauliflower
Here for constructing a 95% confidence interval we have used a One-sample z-test for proportions.
So, 95% confidence interval for the population proportion, p is ;
P(-1.96 < N(0,1) < 1.96) = 0.95 {As the critical value of z at 2.5% level
of significance are -1.96 & 1.96}
P(-1.96 < [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < 1.96) = 0.95
P( [tex]-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < [tex]{\hat p-p}[/tex] < [tex]1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.95
P( [tex]\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < p < [tex]\hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.95
Now, in Agresti and Coull's method; the sample size and the sample proportion is calculated as;
[tex]n = n + Z^{2}__(\frac{_\alpha}{2})[/tex]
n = [tex]24 + 1.96^{2}[/tex] = 27.842
[tex]\hat p = \frac{x+\frac{Z^{2}__(\frac{\alpha}{2}_) }{2} }{n}[/tex] = [tex]\hat p = \frac{2+\frac{1.96^{2} }{2} }{27.842}[/tex] = 0.141
95% confidence interval for p = [ [tex]\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] , [tex]\hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ]
= [ [tex]0.141 -1.96 \times {\sqrt{\frac{0.141(1-0.141)}{27.842} } }[/tex] , [tex]0.141 +1.96 \times {\sqrt{\frac{0.141(1-0.141)}{27.842} } }[/tex] ]
= [0.012, 0.270]
Therefore, a 95% confidence interval for the proportion of students who eat cauliflower on Jane's campus [0.012, 0.270].
The interpretation of the above confidence interval is that we are 95% confident that the proportion of students who eat cauliflower on Jane's campus is between 0.012 and 0.270.
If cos0=-3/5 in quadrant II, what is sin0
Answer:
[tex]\displaystyle \sin \theta = \frac{4}{5}[/tex] if [tex]\displaystyle \cos\theta = -\frac{3}{5}[/tex] and [tex]\theta[/tex] is in the second quadrant.
Step-by-step explanation:
By the Pythagorean Trigonometric Identity:
[tex]\left(\sin \theta\right)^2 + \left(\cos\theta)^2 = 1[/tex] for all real [tex]\theta[/tex] values.
In this question:
[tex]\displaystyle \left(\cos\theta\right)^2 = \left(-\frac{3}{5}\right)^2 = \frac{9}{25}[/tex].
Therefore:
[tex]\begin{aligned} \left(\sin\theta\right)^2 &= 1 -\left(\cos\theta\right)^2 \\ &= 1 - \left(\frac{3}{5}\right)^2 = \frac{16}{25}\end{aligned}[/tex].
Note, that depending on [tex]\theta[/tex], the sign [tex]\sin \theta[/tex] can either be positive or negative. The sine of any angles above the [tex]x[/tex] axis should be positive. That region includes the first quadrant, the positive [tex]y[/tex]-axis, and the second quadrant.
According to this question, the [tex]\theta[/tex] here is in the second quadrant of the cartesian plane, which is indeed above the [tex]x[/tex]-axis. As a result, the sine of this
It was already found (using the Pythagorean Trigonometric Identity) that:
[tex]\displaystyle \left(\sin\theta\right)^2 = \frac{16}{25}[/tex].
Take the positive square root of both sides to find the value of [tex]\sin \theta[/tex]:
[tex]\displaystyle \sin\theta =\sqrt{\frac{16}{25}} = \frac{4}{5}[/tex].
Golden Corral charges $11 for a buffet plus $1 for each drink. Western Sizzlin charges $9 for a buffet plus $2 for each drink. Which restaurant has the best deal? Verify that the intersection point show in your graph is a solution for both equations
Answer:
At 2 drinks, the prices are equal. For 1 drink, Western Sizzlin is better since the buffet price is lower. From 3 drinks and up, Golden Corral is better.
Step-by-step explanation:
"Golden Corral charges $11 for a buffet plus $1 for each drink."
d + 11
"Western Sizzlin charges $9 for a buffet plus $2 for each drink."
2d + 9
Set the 2 cost functions equal:
2d + 9 = d + 11
d = 2
At 2 drinks, the prices are equal. For 1 drink, Western Sizzlin is better since the buffet price is lower. From 3 drinks and up, Golden Corral is better.
Type the correct answer in each box. If necessary, use / for the fraction bar. Complete the statements about series A and B. Series A: 10+4+8/5+16/25+32/125+⋯ Series B: 15+3/5+9/5+27/5+81/5+⋯ Series__ has an r value of___where 0<|r|<1. So, we can find the sum of the series. The sum of the series is___ need help guys please :/
Answer:
Series A has an r value of 2/5 and series A has an r value of 3. The sum of the series A is 50/3
Step-by-step explanation:
A geometric sequence is in the form a, ar, ar², ar³, . . .
Where a is the first term and r is the common ratio = [tex]\frac{a_{n+1}}{a_n}[/tex]
For series A: 10+4+8/5+16/25+32/125+⋯ The common ratio r is given as:
[tex]r=\frac{a_{n+1}}{a_n}=\frac{4}{10} =\frac{2}{5}[/tex]
For series B: 1/5+3/5+9/5+27/5+81/5+⋯ The common ratio r is given as:
[tex]r=\frac{a_{n+1}}{a_n}=\frac{3/5}{1/5} =3[/tex]
For series A a = 10, r = 2/5, which mean 0 < r < 1, the sum of the series is given as:
[tex]S_{\infty}=\frac{a}{1-r}=\frac{10}{1-\frac{2}{5} } =\frac{50}{3}[/tex]
Find m2ABC.
PLZZZ ASAPPPP
Answer:
83
Step-by-step explanation:
You're given two vertical angles, and vertical angles are congruent. This means that (6x - 7) = (4x + 23); x = 15. Plug it into ABC (which is (6x - 7)) to get 6(15) - 7 = 90 - 7 = 83
Please answer it now in two minutes
Answer: 3.2 yd
Step-by-step explanation:
Notice that TWV is a right triangle.
Segment TU is not needed to answer this question.
∠V = 32°, opposite side (TW) is unknown, hypotenuse (TV) = 6
[tex]\sin \theta=\dfrac{opposite}{hypotenuse}\\\\\\\sin 32=\dfrac{\overline{TW}}{6}\\\\\\6\sin 32=\overline{TW}\\\\\\\large\boxed{3.2=\overline{TW}}[/tex]
Below given are the details of transaction of a bank account of three brother Ram, Rahul and Rohit having AED 1000 in each account. a. Ram – Credits AED 500 on 12th May 2020 b. Rahul – Debits AED 700 on 12th May 2020 and Credits AED 500 on 15th May 2020. c. Rohit – Credits AED 700 on 12th May 2002 and Debits AED 500 on 15th May 2020. Who has more amount in his account at the end of the month Arrange the amounts in ascend
Answer:
Ram therefore has more amount in his account at the end of the month, and the balances in their bank accounts at the end of the month are arranged in ascending order, i.e. from the smallest to the largest, as follows:
Rahul – Debits AED 200; Rohit – Credits AED 200; and Ram – Credits AED 500.
Step-by-step explanation:
In banking and finance, a credit transaction on a bank account indicates that an additional amount of money has been added to the bank account and the balance has increased. This gives a positive balance in the account
On the other hand, a debit transaction on a bank account indicates that an amount of money has been deducted or withdrawn from the bank account and the balance has therefore reduced. This gives a negative balance in the account.
Based on the above, we have:
a. Ram – Credits AED 500 on 12th May 2020
Since there is no any other credit or debit transaction during the month, this implies that Ram still has Credits AED 500 in his account at the end of the month.
The Credits AED 500 indicates that Ram has a positive balance of AED 500 in his account at the end of the month.
b. Rahul – Debits AED 700 on 12th May 2020 and Credits AED 500 on 15th May 2020.
The balance in the account of Rahul gives Debits of AED 200 as follows:
Debits AED 700 - Credits AED 500 = Debits AED 200
The Debits AED 200 indicates that Rahul has a negative balance of AED 200 in his account at the end of the month.
c. Rohit – Credits AED 700 on 12th May 2002 and Debits AED 500 on 15th May 2020.
The balance in the account of Rohit gives Credits of AED 200 as follows:
Credits AED 700 - Dedits AED 500 = Credits AED 200
The Credits AED 200 indicates that Rohit has a positive balance of AED 200 in his account at the end of the month.
Conclusion
Arrangement of numbers or amounts of money in ascending order implies that they are arranged from the smallest to the largest number or amount.
Since Credits implies positive amount and Debits implies negative amount, Ram therefore has more amount in his account at the end of the month, and the balances in their bank accounts at the end of the month are arranged in ascending order, i.e. from the smallest to the largest, as follows:
Rahul – Debits AED 200; Rohit – Credits AED 200; and Ram – Credits AED 500.
Find the measure of angle A associated with the following ratios and round to the nearest degree. CosA=0.2785 m∠A=
Answer:
74°.
Step-by-step explanation:
From the question given above,
Cos A = 0.2785
To get the value of angle A, we simply find the inverse of Cos as shown below:
Cos A = 0.2785
Take the inverse of Cos.
A = Cos¯¹ 0.2785
A = 73.8° ≈ 74°
Therefore, the value of angle A is approximately 74°
ASAP! I really need help with this question! Please do not send nonsense answers. Full solutions please!
Answer:
first option
Step-by-step explanation:
Given
[tex]\frac{15}{x}[/tex] + 6 = [tex]\frac{9}{x^2}[/tex]
Multiply through by x² to clear the fractions
15x + 6x² = 9 ( subtract 9 from both sides )
6x² + 15x - 9 = 0 ( divide through by 3 )
2x² + 5x - 3 = 0 ← in standard form
Consider the factors of the product of the coefficient of x² and the constant term which sum to give the coefficient of the x- term.
product = 2 × - 3 = - 6 and sum = + 5
The factors are + 6 and - 1
Use these factors to slit the x- term
2x² + 6x - x - 3 = 0 ( factor the first/second and third/fourth terms )
2x(x + 3) - 1(x + 3) = 0 ← factor out (x + 3) from each term
(x + 3)(2x - 1) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 3 = 0 ⇒ x = - 3
2x - 1 = 0 ⇒ 2x = 1 ⇒ x = 0.5
Solution set is { - 3, 0.5 }